On the metabelian local Artin map I: Galois conjugation law
Turkish Journal of Mathematics, cilt.24, sa.1, ss.25-58, 2000 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 1
- Basım Tarihi: 2000
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.25-58
- Anahtar Kelimeler: Local fields, Metabelian extensions, Metabelian local Artin map, Non-abelian local class field theory
- Boğaziçi Üniversitesi Adresli: Hayır
Özet
It is proved that, for a (henselian) local field K and for a fixed Lubin-Tate splitting φ over K, the metabelian local Artin map (?, K) φ : ℜ(K,φ)→̃Gal(K(ab)2/K) satisfies the Galois conjugation law (σ̃+(α), σ(K)) σ̃φσ̃-1 = σ̃|K (ab)2(α, K)φσ̃-1| σ̃(K(ab)2) for any α ∈ ℜ(K, φ), and for any embedding σ : K Ksep, where σ̃ ∈ Aut (Ksep) is a fixed extension to Ksep of the embedding σ : K Ksep. © TÜBİTAK.